Find the central angle of a sector of a circle if the area of the circle and the area of the sector are in the proportion of 5:3 ( with explanation )

216 degrees

Step-by-step explanation:

The area of a circle = πr^2 while

The area of a sector = θ/360 × πr^2

 if the area of the circle and the area of the sector are in the proportion of 5:3,

Then, area of a circle divided by the area of a sector will be equal to 5/3. That is,

πr^2 ÷ θ/360 × πr^2 = 5/3

πr^2 ÷ θπr^2/360 = 5/3

πr^2 × 360/ θπr^2 = 5/3

πr^2 will cancel out. Leading to

360/θ = 5/3

Cross multiply and make θ the subject of formula

5θ = 3 × 360

θ = 1080/5

θ = 216 degrees

Therefore, the central angle of a sector of a circle is 216 degrees

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.